Phi - Use As A Symbol

Use As A Symbol

The lower-case letter φ (or often its variant, ϕ) is often used to represent the following:

• The golden ratio in mathematics, art, and architecture.
• Euler's totient function φ(n) in number theory; also called Euler's phi function.
• In algebra, group or ring homomorphisms
• In probability theory, ϕ(x) = (2π)−½e−x2/2 is the probability density function of the normal distribution.
• In probability theory, φ_X(t) = E is the characteristic function of a random variable X.
• An angle, typically the second angle mentioned, after θ (theta). Especially:
  • The argument of a complex number.
  • The phase of a wave in signal processing.
  • In spherical coordinates, mathematicians usually refer to phi as the polar angle (from the z-axis). The convention in physics is to use phi as the azimuthal angle (from the x-axis).
  • One of the dihedral angles in the backbones of proteins.
  • Internal or effective angle of friction.
• The work function in electronics.
• A shorthand representation for an aromatic functional group in organic chemistry.
• The fugacity coefficient in thermodynamics.
• The ratio of free energy destabilizations of protein mutants in phi value analysis.
• In cartography and navigation, latitude.
• In combustion engineering, equivalence ratio. The ratio between the actual fuel air ratio to the stoichiometric fuel air ratio.
• A sentence in first-order logic.
• Porosity in geology and hydrology.
• Strength (or resistance) reduction factor in structural engineering, used to account for statistical variabilities in materials and construction methods.
• The symbol for a voiceless bilabial fricative in the International Phonetic Alphabet (using the straight line variant character)
• In economics, this is usually an additive term.
• In flight dynamics, the roll angle.
• In philosophy, φ is often used as shorthand for a generic act. (Also in upper-case.)

The upper-case letter Φ is used as a symbol for:

• The golden ratio conjugate −0.618... in mathematics.
• The magnetic flux and electric flux in physics, with subscripts distinguishing the two.
• The cumulative distribution function of the normal distribution in mathematics and statistics.
• In philosophy, Φ is often used as shorthand for a generic act. (Also in lower-case.)
• The number of phases in a power system in electrical engineering, for example 1Φ for single phase, 3Φ for three phase.
• A common symbol for the parametrization of a surface in vector calculus.
• In Lacanian algebra, Φ stands for the imaginary phallus and also represents phallic signification. -Φ stands in for castration.

The diameter symbol in engineering, ⌀, is often incorrectly referred to as "phi". This symbol is used to indicate the diameter of a circular section, for example "⌀14", means the diameter of the circle is 14 units.